Question

Determine which ordered pair (s) are solutions to the following system.

(x-2y=4),(x-y=0): (2,3) (-4,-4) (4,1)

Answer 1

To determine which ordered pairs are solutions to the system of linear equations, we substitute each ordered pair into both equations. After checking, we find that only the ordered pair (-4,-4) is a solution to the given system.

Step-by-step explanation:

To determine which ordered pairs are solutions to the system of equations (x-2y=4), (x-y=0), we need to substitute the x and y values from each ordered pair into both equations and check for their validity.

Steps for each ordered pair:

Substitute the x and y values into both equations.

1. If both equations are true, the ordered pair is a solution to the system.

Let's check each:

• (2,3): Substituting into the first equation 2-2(3)=4 gives -4=4, which is false. Substituting into the second equation 2-3=0 gives -1=0, which is also false. So, (2,3) is not a solution.
• (-4,-4): Substituting into the first equation -4-2(-4)=4 gives 4=4, which is true. Substituting into the second equation -4-(-4)=0 gives 0=0, which is true. Therefore, (-4,-4) is a solution.
• (4,1): Substituting into the first equation 4-2(1)=4 gives 2=4, which is false. Substituting into the second equation 4-1=0 gives 3=0, which is also false. Hence, (4,1) is not a solution.